Rayleigh damping in the free troposphere

Moist convection is shown to produce damping and descent of passive tracers and horizontal wind. Analytical expressions are derived for the damping timescale and descent speed, and these are found to depend on the vertical wavelength of the profile. These results predict that short wavelengths damp faster and descend faster than long wavelengths, and these predictions are confirmed using large-eddy simulations. Large wavelengths can be approximated as damping in place, which can be described with a wavelength-dependent Rayleigh damping or a wavelength-independent viscosity. For large wavelengths, the effective diffusivity of tracers is proportional to the mass flux divided by the fractional entrainment rate. For the deeply convecting tropics, this free-tropospheric diffusivity is estimated to be in the range of 10-30 m²/s. The effective viscosity is somewhat smaller due to the pressure-gradient force on rising clouds, but the effective Rayleigh damping is still significant for small and intermediate vertical wavelengths. For an intermediate vertical wavelength of six kilometers, a wind profile experiences Rayleigh damping on a timescale of 1 to 10 days over a majority of the tropical ocean.